LillieforsTest Class

[SerializableAttribute]
public class LillieforsTest : HypothesisTest<EmpiricalDistribution>, 
	IHypothesisTest<EmpiricalDistribution>, IHypothesisTest

<SerializableAttribute>
Public Class LillieforsTest
	Inherits HypothesisTest(Of EmpiricalDistribution)
	Implements IHypothesisTest(Of EmpiricalDistribution), IHypothesisTest

// Test against a Uniform distribution fitted from the data

// Make this example reproducible
Accord.Math.Random.Generator.Seed = 1;

// Suppose we got a new sample, and we would like to test whether this
// sample seems to have originated from a uniform continuous distribution.
// 
double[] sample =
{
    0.021, 0.003, 0.203, 0.177, 0.910, 0.881, 0.929, 0.180, 0.854, 0.982
};

// First, we create the distribution we would like to test against:
// 
var distribution = UniformContinuousDistribution.Estimate(sample);

// Now we can define our hypothesis. The null hypothesis is that the sample
// comes from a standard uniform distribution, while the alternate is that
// the sample is not from a standard uniform distribution.
// 
var lillie = new LillieforsTest(sample, distribution, iterations: 10 * 1000 * 1000);

double statistic = lillie.Statistic; // 0.36925
double pvalue = lillie.PValue; // 0.09057

bool significant = lillie.Significant; // false

// Since the null hypothesis could not be rejected, then the sample
// can perhaps be from a uniform distribution. However, please note
// that this doesn't means that the sample *is* from the uniform, it
// only means that we could not rule out the possibility.

// Test against a Normal distribution

// Make this example reproducible
Accord.Math.Random.Generator.Seed = 1;

// This time, let's see if the same sample from the previous example
// could have originated from a fitted Normal (Gaussian) distribution.
// 
double[] sample = 
{
    0.021, 0.003, 0.203, 0.177, 0.910, 0.881, 0.929, 0.180, 0.854, 0.982
};

// Before we could not rule out the possibility that the sample came from
// a uniform distribution, which means the sample was not very far from
// uniform. This would be an indicative that it would be far from what
// would be expected from a Normal distribution:

NormalDistribution distribution = NormalDistribution.Estimate(sample);

// Create the test
var lillie = new LillieforsTest(sample, distribution);

double statistic = lillie.Statistic; // 0.2882
double pvalue = lillie.PValue; // 0.0207

bool significant = lillie.Significant; // true

// Since the test says that the null hypothesis should be rejected, then
// this can be regarded as a strong indicative that the sample does not
// comes from a Normal distribution, just as we expected.